Gauge invariance in quantum hadrodynamics

This paper describes the derivation of a new representation of an SU(2)L× SU(2)R locally-invariant model of the strong interactions called quantum hadrodynamics 3 (QHD-III). QHD-III is a gauge-invariant theory based on the linear σ model, the gauge bosons being the ρ and the a1. The new representation considerably simplifies the lagrangian. To derive the new representation, the gauge invariance of the model is exploited. The role of the gauge boson masses in gauge-invariant models of the strong interactions based on the σ model is also discussed, and it is shown that these masses are necessary if the pion is to survive as a physical field. Hadronic models have had significant phenomenological success in describing the manybody strongly interacting system at low energies [1]. These models take hadrons as their effective degrees of freedom. The lagrangians of hadronic models are constructed in such a way that they reflect the symmetries of QCD, while incorporating low-energy phenomenology. In particular, these models must give rise to conserved vector and partially conserved axial-vector currents, and they should include the exchange of mesons which are known to carry the strong force at low energies. The mesons should be introduced such that corrections coming from meson loops are consistently calculable within the model. Since there is a large number of mesons, any model based on meson exchange must find a consistent way to choose the relevant mesons; this can be achieved by introducing them as gauge bosons.